Multi-strain persistence induced by host age structure

In this paper, we formulate an age-structured epidemic model with two competing strains. The model incorporates disease-induced mortality so that the population cannot be assumed to be in a stationary demographic state. We derive explicit expressions of the basic and invasion reproduction numbers for strain one and two, respectively. Analytical results of the model show that the existence and local stability of boundary equilibria can be determined by the reproduction numbers to some extent. Subsequently, under the condition that both invasion reproduction numbers are larger than one, the coexistence of two competing strains is rigorously proved by the theory of uniform persistence of infinite dimensional dynamical systems. However, the results for the corresponding age-independent model show that the two competing strains cannot coexist. This implies that age-structure can lead to the coexistence of the strains. Numerical simulations are further conducted to confirm and extend the analytic results.